According to the United States Census Bureau, the city has a total area of 2.1 square miles (5.4 km²), which is 99% land.
There were 439 households out of which 30.5% had children under the age of 18 living with them, 56.3% were married couples living together, 6.8% had a female householder with no husband present, and 32.8% were non-families. 30.1% of all households were made up of individuals and 16.2% had someone living alone who was 65 years of age or older. The average household size was 2.39 and the average family size was 2.97.
In the city the population was spread out with 25.1% under the age of 18, 7.3% from 18 to 24, 23.1% from 25 to 44, 22.3% from 45 to 64, and 22.2% who were 65 years of age or older. The median age was 41 years. For every 100 females there were 94.3 males. For every 100 females age 18 and over, there were 93.6 males.
The median income for a household in the city was $30,682, and the median income for a family was $37,273. Males had a median income of $30,066 versus $18,214 for females. The per capita income for the city was $16,859. About 9.3% of families and 13.0% of the population were below the poverty line, including 17.2% of those under age 18 and 4.4% of those age 65 or over.
The first endeavor to establish a town below the junction of the rivers, in 1857, failed due to misfortunes of two of the three participants. No further attempt to utilize the impressive water power was made until 1869–1870, when a colony of about 50 families from Genesee County, New York moved in, purchased land and water power rights, and began establishing a community. The Blue Rapids Town Company was formed, and by the end of 1870 the population was about 250. In 1872, Blue Rapids was incorporated as a city of third class under the statutes of Kansas.
Among the first projects in 1870 were a stone dam and a wrought iron bridge built on the Big Blue River. A hydroelectric power plant was then added to provide power for manufacturing and for the town. The power plant was destroyed by a flood in 1903. In the late 1800s and early 1900s there were four gypsum mines in the area. The population peaked around 1910 at over 1,750. The public library, built in 1875, is the oldest library west of the Mississippi in continuous operation in the same building.
Blue Rapids was the birthplace of the pancreatic cancer drug Streptozotocin. The bacterium from which the drug is derived was discovered in the late 1950s in a soil sample taken from "an uncultivated sandy soil in a grassland region" at Blue Rapids.
Blue Rapids claims to be the smallest town in the U.S. to have hosted a national league baseball game. On October 24, 1913, more than 3,000 fans watched the Chicago White Sox and New York Giants play a world tour exhibition game on the local ball field that is still in use today.